Interpreting membrane scattering experiments at the mesoscale: the contribution of dissipation within the bilayer

Neutron spin-echo spectroscopy provides a means to study membrane undulation dynamics over length scales roughly spanning 10-100 nanometers. Modern interpretation of these measurements relies on the theoretical predictions of Zilman and Granek; however, it is necessary to introduce an anomalously large solvent viscosity within this theory to obtain quantitative agreement with experiment. An extended theoretical treatment is presented that includes the effects of internal dissipation within the bilayer. Within the length and time regimes appropriate to neutron spin-echo experiments, the results of Zilman and Granek are largely recovered, except that the bilayer curvature modulus kappa appearing in their theory must be replaced with an effective dynamic curvature modulus kappa =kappa+2d(2)k(m), where d is a distance comparable to the monolayer thickness (the height of the neutral surface from bilayer midplane) and k(m) is the monolayer compressibility modulus. Direct comparison between theory and experiment becomes possible without any rescaling of physical parameters.